LCM of fractions with coprime denominators: Compute the LCM of 2/3, 3/5, 4/7, and 9/13 using the LCM(numerators)/GCD(denominators) rule.

Introduction / Context:
For fractions, LCM = LCM of numerators divided by GCD of denominators. When denominators are pairwise coprime overall (GCD = 1), the LCM simplifies to just the LCM of numerators as an integer.

Given Data / Assumptions:

• Fractions: 2/3, 3/5, 4/7, 9/13.
• All denominators 3, 5, 7, 13 are pairwise coprime, so overall GCD is 1.

Concept / Approach:
Compute LCM of numerators 2, 3, 4, 9. Then divide by GCD of denominators (which is 1), meaning the LCM is simply that numerator LCM.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 1/36 and 1/1365 are reciprocals-like values, not suitable here.
• 12/455 does not produce integer quotients with all given fractions.

Common Pitfalls:

• Treating the LCM of denominators instead of their GCD for the fraction-LCM formula.

Final Answer: